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Magneto-induced large deformation and high-damping performance of a magnetorheological
plastomer
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2014 Smart Mater. Struct. 23 105028
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Smart Materials and Structures
Smart Mater. Struct. 23 (2014) 105028 (10pp)
doi:10.1088/0964-1726/23/10/105028
Magneto-induced large deformation and
high-damping performance of a
magnetorheological plastomer
Taixiang Liu, Xinglong Gong, Yangguang Xu, Haoming Pang and
Shouhu Xuan
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics,
University of Science and Technology of China, Hefei, 230027, People’s Republic of China
E-mail: [email protected]
Received 24 April 2014, revised 23 July 2014
Accepted for publication 6 August 2014
Published 16 September 2014
Abstract
A magnetorheological plastomer (MRP) is a new kind of soft magneto-sensitive polymeric
composite. This work reports on the large magneto-deforming effect and high magneto-damping
performance of MRPs under a quasi-statical shearing condition. We demonstrate that an MRP
possesses a magnetically sensitive malleability, and its magneto-mechanical behavior can be
analytically described by the magneto-enhanced Bingham fluid-like model. The magnetoinduced axial stress, which drives the deformation of the MRP with 70 wt % carbonyl iron
powder, can be tuned in a large range from nearly 0.0 kPa to 55.4 kPa by an external
662.6 kA m−1 magnetic field. The damping performance of an MRP has a significant correlation
with the magnetic strength, shear rate, carbonyl iron content and shear strain amplitude. For an
MRP with 60 wt % carbonyl iron powder, the relative magneto-enhanced damping effect can
reach as high as 716.2% under a quasi-statically shearing condition. Furthermore, the related
physical mechanism is proposed, and we reveal that the magneto-induced, particle-assembled
microstructure directs the magneto-mechanical behavior of the MRP.
Keywords: magnetorheological plastomer, magneto-damping effect, magneto-mechanical
behavior
(Some figures may appear in colour only in the online journal)
1. Introduction
themselves due to the constraint of the matrix. However,
when an external magnetic field is applied to an MRP, the
internal particles will overcome the constraint of the matrix
and can rearrange into some ordered microstructures. The
ordered microstructures will be kept in the MRP while the
external magnetic field is switched off or removed. Correspondingly, it is worth noting that the microstructure-based
physical properties (e.g. the electric conductivity, thermal
conductivity, acoustic conductivity, etc) of the MRP change
significantly once the external field is removed. These conducting properties are vital in practical sensors and actuators.
With its novel performance in magnetorheology, MRPs are
very promising for use as a new or alternative material in
many practical applications, such as magneto-dampers
[10–12], energy absorbers [13, 14] and vibration isolators
A magnetorheological plastomer (MRP) is a new kind of soft
magneto-sensitive polymeric composite material, which has a
novel performance in magnetorheology [1]. In the usual way,
an MRP is prepared by dispersing micron-sized magnetic or
magnetizable particles into magnetically insensitive, soft
polymer matrixes. An MRP behaves as an intermediate state
between traditional fluid-like magnetorheological fluid (MRF)
[2–6] and conventional solid-like magnetorheological elastomers (MREs) [7–9]. In contrast to the easily sedimentary
MRF and the relatively low- magnetorheological-effect MRE,
an MRP attractively possesses long-time stability and a higher
magnetorheological effect. Under usual conditions, the
internal magnetizable particles in an MRP cannot move by
0964-1726/14/105028+10$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
polypropylene glycol (PPG-1000, Sigma-Aldrich Trading Co.
Ltd, Shanghai, China) with the ratio 3:1. We mixed the raw
materials into a three-necked round-bottom flask at 75 °C and
then stirred the mixture for 2 h. Subsequently, we lowered the
temperature of the mixture to 65 °C and dropwise added a
small quantity of stannous octoate and a moderate amount of
acetone (both provided by Sinopharm Chemical Reagent Co.
Ltd, China) into the flask to accelerate the cross-linking
reaction and avoid gelating. Twenty minutes later, the
synthesis process of the matrix was finished. Once the matrix
was synthesized, we immediately added a soft magnetic
powder into the matrix and adequately blended the mixture
before cooling the matrix down; thus, the MRP sample was
prepared.
In our experiment, we added soft-magnetic carbonyl iron
powder (CIP, type CN, 7.200 g · cm−3 in true density, produced by BASF aktiengesellschaft, Germany) into the prepared plastic polyurethane matrix (0.986 g · cm−3 in density)
with the CIP’s weight ratio of 40%, 50%, 60% and 70% in the
mixture to the volume fraction of 8.4%, 12.0%, 17.0%, and
24.2% of the carbonyl iron powder, respectively, in the
mixture. Correspondingly, we denote these samples as MRP40, MRP-50, MRP-60 and MRP-70, respectively.
[15, 16], especially in magneto-sensitive sensors and actuators [17–19], etc.
A typical soft polyurethane-based MRP composited with
carbonyl iron powder was prepared and reported in our
group’s previous work [1]. It was shown that the chain-like
microstructure was formed when an external magnetic field
was applied to an MRP, and the microstructure was kept in
the MRP after switching off the external magnetic field.
Conventional magnetic sweep tests were implemented to
study the dynamic properties of the MRP and showed that the
magneto-induced storage modulus and the relative magnetorheological effect of the MRP with 80% carbonyl iron
powder could respectively reach as high as 6.54 MPa and
532% under an external 662.6 kA m−1 magnetic field. In
addition, the static time-dependent creep and recovery behaviors of the MRP and the dynamic behavior of the MRP
under oscillatory shear rheometry were systematically investigated [20, 21] and provided a certain reference to the design
and development of applicatory devices for static and
dynamic cases, respectively. However, it is still necessary to
point out that many practical damping or actuating apparatuses work in the case of large deformation and quasi-static
shear such as in bridge engineering, high-rise building engineering, vehicle system control, etc. The quasi-static loading
rate is neither a static rate nor a dynamic rate, but it serves as a
bridge between the static and dynamic loading rates. The
magneto-damping performance of apparatuses partly depends
on the magneto-deforming capacity of the useable material.
For these apparatuses, the material with the larger magnetodeforming capacity and higher magneto-damping performance is much needed. The magneto-mechanical behavior of
the useable material has a great effect on the performance of
the apparatuses; therefore, for the high-performance MRP, it
is imperative to study its magneto-deforming effect and
magneto-damping performance under cyclically and quasistatically shearing conditions and to understand the relative
physical mechanism.
This work focuses on the magneto-induced large deformation effect of MRPs and the magneto-damping performance of MRPs under cyclically and quasi-statically shearing
conditions. Firstly, a sample of magneto-induced large
deformation is intuitively given, and the related magnetoinduced stress in the MRP is discussed. Then, the magnetodamping performance of the MRP under a cyclically and
quasi-statically shearing condition with different samples,
shear rates and strain amplitudes in the absence/presence of
an external magnetic field are investigated. Correspondingly,
the microstructure-based physical mechanisms of these
behaviors are further discussed according to the relative
experimental results.
3. Magneto-induced large deformation of an MRP
For a magneto-sensitive and shape-changeable MRP, it is
interesting to explore the shape-changing process of an MRP
with different initial shapes and/or under a different magnetic
field. If the exterior shape-change of the material is of prime
interest, Digital Image Correlation (DIC) and interferometry
techniques provide the user with mature experimental
approaches that may meet the demand [22]. It is also commonly known that a basic mechanical behavior always drives
the deformation of the material. However, it is difficult or
impossible to simultaneously measure the deformation of the
material and the relative mechanical behavior. Recently,
magneto-induced normal (or axial) force/stress in an MRF
[23, 24] and in magnetorheological gel [25–27] under axially
constrained and/or slow loading conditions were well studied,
providing us with useful references.
To explore the magneto-induced large deformation of an
MRP, we chose MRP-70 as a test sample and used a commercial magnetic field generator (S&T Tech. Inc., Beijing,
China) to generate the desired magnetic field. As shown in
figure 1(a), we firstly shaped the MRP-70 into a small sphere
and put it into the magnetic field generator; then, we quickly
switched on a 585 kA m−1 magnetic field (i.e. about 735 mT
in magnetic intensity). Thirty seconds later, the initiated
sphere shape changed into a shuttle-like shape (figure 1(b)).
Meanwhile, the shuttle-shaped MRP-70 connected the upper
and lower magnetic poles into a magnetic conducting channel. When the current of the upper magnetic pole would be
switched off, the shuttle-shaped MRP-70 would shrink back
to the lower pole. This delaying connecting and shrinking
effect makes MRPs promising for switches in situations in
which avoiding destructive impact is needed. We shaped the
2. Experimental
To prepare the MRP sample, a visco-flowing plastic matrix
must first be synthesized. The matrix can be synthesized from
toluene diisocyanate (TDI, 2,4-TDI at ∼80%, 2,6-TDI at
∼20%, Tokyo Chemical Industry Co. Ltd, Japan) and
2
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
a
b
0s
c
30 s
d
e
−1
Figure 1. The large deformation of the magneto-sensitive MRP-70 under a uniform 585 kAm magnetic field. In the upper series, the small
sphere-shaped MRP-70 at an initial 0 s (a) changes its shape into a shuttle-like shape at 30 s (b). In the lower series, the initial oblate shape of
MRP-70 (c) is changed into a parallel column-like shape (e) by the external magnetic field.
MRP-70 into an oblate shape (figure 1(c)) and placed it into
the magnetic field generator (figure 1(d)); it was apparent that
the MRP-70 gradually swelled considerably along the direction of the magnetic field (figure 1(e)) after a 585 kA m−1
magnetic field was switched on. For an incompressible
material, the MRP’s volume barely changes when the external
magnetic strength is varied. However, the internal particleassembled microstructure is magnetically field-dependent.
This dependence causes the morphology of the MRP to
change along with the external magnetic field, and it contributes to the directional swell. The swelling effect makes the
MRP applicable as a force actuator in vibration control or
others, not only for slow or delay actuating but also for quick
actuating. This will be discussed below.
To study the magneto-induced stress of an MRP, we used
a commercial rheometer Physica MCR301 (produced by
Anton Paar GmbH, Austria) equipped with an electromagnetic accessory MRD180 to do the test. The sketch of the
test system is shown in the inset of figure 2. The MRP sample
is placed between an electromagnet substratum and an upper
rotatable non-magnetism plate (i.e. the rotor). Here, we define
the vertical direction perpendicular to the substratum as the
normal direction. The magnetizer cover is used to strengthen
the magnetic field and make it uniform in the area in which
the sample is placed. The following experiments were all
conducted at room temperature 25 °C.
The magneto-induced normal stress σn of the MRP that
evolved with the slow-loading external magnetic field is
shown in figure 2. In the tests, the strength of the magnetic
field increases linearly from an initial 0.0 kA m−1 to a final
293.0 kA · m−1 in 60 min. However, the magneto-normal
stress does not increase linearly along with the increasing
magnetic strength. When the magnetic strength is smaller than
50.0 kA m−1 (as the dash-dot arrow indicates in figure 2), the
magneto-normal stress barely changes with the increasing the
Figure 2. Magneto-induced normal stress σn of the MRP that evolves
with the slow loading of the external magnetic field. The inset is the
sketch of the Physica MCR301 test system.
magnetic strength. The magneto-normal stress linearly
increases along with the increasing magnetic strength when
the magnetic strength is greater than 50.0 kA m−1. When an
external 662.6 kA m−1 magnetic field is suddenly applied, the
magneto-stress gets a sudden increment in the beginning and
then gradually plateaus (as figure 3 shows) with time. The
microstructural evolution that relates to the evolving magneto-induced normal stress has been studied in our previous
work [28, 29]. As shown in the inset of figure 3, the internal
particle-formed microstructure evolves from initial random
dispersion (figure 3(a)) to an unstable chain-like structure
(figure 3(b)) and then to a stable column-like structure
(figure 3(c)). The macroscopic magneto-induced normal
stress results from interparticle attraction and extrusion along
the magnetic field’s direction, and the magnitude of the stress
can reach as high as 55.4 kPa. Moreover, one can clearly
3
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
Figure 4. The shear stress-strain curves of the MRP-60 with (right)
and without (left) an external magnetic field under different
shearing-rate conditions. Respectively, the inset shows the MRP’s
analytical models in the absence and presence of an external
magnetic field.
Figure 3. Magneto-induced normal stress σn of the MRP that evolves
with the transient loading of the external 662.6 kAm−1 magnetic
field. The insets show the internal microstructure of the MRP, which
progresses from initial random dispersion (a) to an unstable chainlike configuration (b) and then to a stable column-like pattern (c).
times of 0.5 s, 1.5 s, 3.0 s, 6.0 s, 12.0 s, 25.0 s, 50.0 s, 100.0 s
and 200.0 s, respectively. The corresponding shear rates in the
test are labeled in the right side of figure 4.
In the absence of an external magnetic field (i.e. the
external magnetic strength H = 0.0 kA m−1), the shear stress τ
gets a sudden increment at the beginning and then plateaus in
a short time with the enlargement of the shear strain. This
mechanical behavior can be described using the conventional
viscoelastic-plastic Bingham fluid-like model:
determine that the carbonyl iron content in an MRP can
greatly affect the magneto-induced stress. From the above two
tests, one can see that the MRP has great potential for use in a
force actuator for either slow or quick actuating.
4. Magneto-damping performance of an MRP under a
quasi-statically shearing condition
⎧ G0 γ + ηγ ,̇ for γ < γ0
τ=⎨
⎩ G0 γ0 + ηγ ,̇ for γ ⩾ γ0
In practice, damping materials usually work in the quasi-static
shearing mode for vibration control or for anti-seismic
applications such as in bridge engineering, high-rise building
engineering, vehicle system control, etc. As a recently
reported smart magnetorheological material, a high-performance MRP shows attractive potential for the above-mentioned practical applications. However, the mechanical
behaviors of an MRP under cyclically and quasi-statically
shearing conditions have not been studied until now. Given
this information, the following work will focus on the MRP’s
mechanical behavior under a quasi-statically shearing condition with different CIP contents, shearing rates and strain
amplitudes in the absence/presence of external magnetic
strength. The tests were conducted with a Physica MCR301
rheometer, and the temperature in each test was stably controlled at 25 °C.
(1)
in which, τ is the shear stress, G0 is the initial shear modulus,
γ is the shear strain, γ0 is the yield shear strain, η is the
equivalent flowing viscosity and γ ̇ is the shear rate. The
equivalent analytical model of this mechanical behavior is
shown as the inset of figure 4 (in ‘H = 0.0 kA m−1’), which is
constructed by a dashpot that is parallel to a cascade of a
spring and a slider. γ0 and G0 reflect the MRP’s initial elasticity, including the elasticity of the polyurethane matrix, the
elasticity of the carbonyl iron particle and the elastic interaction between the matrix and the particle. After the yield, the
mechanical behavior of the MRP can be characterized by η,
which depends on the flow of the matrix itself and the relative
slip between the matrix and the particle. From the experimental results, the values of γ0, G0, and η in the analytic
model can be estimated in the order of 5.0%, 15.0 kPa and
107.8 kPa · s (when the shear rate is γ ̇ = 0.083 s−1), respectively, which indicates that the MRP-60 is a high-viscosity
material with a certain low-yield strength. One can determine
that the MRP-60 possesses good plastic malleability and
behaves in a highly rate-dependent manner.
In the presence of an external magnetic field (i.e.
H = 293.0 kA m−1), the mechanical shear stress-strain behavior of the MRP-60 under different shearing conditions can be
seen from the right subfigure of figure 4. Before the test, a
662.6 kA m−1 magnetic field is applied and kept for 300 s to
4.1. Mechanical behavior under a simple shearing condition
Considering that the MRP prospectively works in a quasistatic shearing mode, the basic rate-dependent shear stressstrain curve of the MRP is tested and discussed. For example,
the shear stress-strain curves of the MRP-60 under different
shearing-rate conditions with/without an external magnetic
field are presented in figure 4. In the test, the shear strain
progresses linearly from an initial 0% to 100% in the different
4
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
adequately preconfigure the internal particle-formed microstructure in the MRP-60. One can see that the shear stress also
gets a sudden increment at the beginning of the shear strain’s
progress; however, the shear stress then linearly and continuously increases with the increasing shear strain. This
progress of the shear stress-strain behavior greatly differs to
that in the absence of an external magnetic field. Here, it can
clearly be seen that a plateau occurs when the shear rate is
larger than 0.333 s−1; this is because the shear stress, which is
needed to overcome the yield stress and drive the flow of the
MRP-60, exceeds the friction stress between the test plate and
the MRP-60 sample. That is to say, slipping occurs at the
contact interface between the test plate and the sample. Given
this information, the following discussion will only focus on
the test results when the shear rate is less than or equal to
0.333 s−1. To describe the mechanical behavior of the MRP
under an external magnetic field, a modified Bingham fluidlike model is proposed as:
⎧
⎪ G0 γ + Gm γ + ηm + η γ ,̇ for γ < γ0
τm = ⎨
.
⎪
⎩ G0 γ0 + Gm γ + ηm + η γ ,̇ for γ ⩾ γ0
(
(
)
)
Figure 5. The shear stress-strain curves of different MRP samples
under constant shear rate |γ| = 0.040 s−1 and strain amplitude
A0 = 100% without an external magnetic field. The top-left inset
shows the analytical model of the MRP.
(2)
quasi-statically shearing condition. In the following work, we
will firstly study the effect of CIP content in an MRP; then,
the effect of the shear rate and the effect of the strain
amplitude on a certain MRP sample, respectively, will be
discussed. The following comparative tests are at the core of
the MRP-60, with a shear rate of γ ̇ = 0.040 s−1 and a shear
strain amplitude of A0 = 100%; we mark this test as (MRP-60,
γ ̇ = 0.040 s−1, A0 = 100%).
The effect of the CIP content on the mechanical behavior
can be seen in figure 5. In all of the tests, the magnitude of
shear rate γ ̇ is set as a constant of 0.040 s−1, and shear strain
amplitude A0 is set as 100%. The shear strain progresses
linearly from an initial 0% to 100% with the shear rate of γ ̇
= 0.040 s−1; then, it immediately shifts back from 100% and
inversely appoaches −100% with a constant shear rate of
−0.040 s−1. Then, the shear strain gruadually returns to 0%
again from −100% with the shear rate 0.040 s−1. Correspondingly, the shear stress gets a sudden increment at the
beginning and then approaches a stable value at about
γ = 25%. After the shear strain gets the maximum (inverse
maximum) γ = 100% (−100%), the shear stress will inversely
get a abrupt drop (rise); then, it becomes stable at about
γ = 50%. The shear stress-strain curve draws a gapped hysteresis loop (directly referred to as ‘loop’ in the following
context). The analytical model of this mechanical behavior
can be discribed as the inset of figure 5. In figure 5, the area
between the shear stress-strain curve and the horizontal axis
denotes the density of the energy that is absorbed by the MRP
during a cyclical process of shear strain. The larger the area,
the more the energy absorption, and the stronger the MRP’s
damping. From figure 5, we can quantitively compare the
sizes of the areas of MRP-40, MRP-50, MRP-60 and MRP-70
using the following integration:
Here, τm is the shear stress in the presence of the external
magnetic field, Gm is the magneto-induced shear modulus and
ηm is the magneto-induced viscosity. The equivalent analytical
model of this mechanical behavior can be recognized as a
parallel combination of three elements: a magnetic relevant
dashpot, a magnetic dependent spring and a spring-slider. Gm
results from the interparticle magnetic interaction, which
depends on the strength of the external magnetic field and the
internal particle-assembled microstructure of the MRP. The
interparticle magnetic interaction resists the shear deformation
of the MRP and persistently contributes to the strength of the
shear modulus. Similarly, the interparticle magnetic interaction resists the flow of the MRP in the post-yield range and
enhances the effective viscosity of the MRP, introducing a
magneto-induced increment of viscosity ηm . According to the
experimental results, the value of Gm and ηm can be estimated
on the order of 20.2 kPa and 119.4 kPa · s (when the shear rate
is γ ̇ = 0.083 s−1), respectively. Considering the initial shear
modulus G0 = 15.0 kPa) and the viscosity η = 107.8 kPa · s of
the MRP-60 under no external magnetic field, one can
determine that the external magnetic field can substantially
affect the property of an MRP. Similar works on the modeling
of the field-induced plasticity and magneto-dipolar striction of
soft magnetic elastomers were well done [30–32].
4.2. Mechanical behavior under a cyclically shearing condition
without an external magnetic field
In a low-frenquency damper, the damping material usually
works under a cyclically shearing condition in a passive mode
without an external magnetic field. The performances of a
damper, such as the strength of the resistance and the capacity
of the energy absorption, directly depend on the mechanical
behavior of the damping material. Thus, for the prospective
damping material of the MRP, it is imperative to study the
basic mechanical behavior of the MRP under a cyclically and
ρE =
5
∮ τdγ = ∫0
A0
−A 0
τd γ +
∫A
0
τd γ +
0
∫−A
τd γ .
0
(3)
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
Figure 6. The shear stress-strain curve of the MRP-60 under a
Figure 7. The shear stress-strain curve of the MRP-60 under a
different shear rate and constant strain amplitude A0 = 100% without
an external magnetic field.
different strain amplitude and a constant shear rate |γ| = 0.040 s−1
without an external magnetic field.
Here, A0 is the shear strain amplitude 100%, τ is the
shear stress in the absence of an external magnetic field, γ is
the shear strain, and correspondingly the sizes of the areas or
the density of the absorbed energy ρE = 10.23, 21.34, 27.82
and 44.71 kJ · m−3, respectively. Thus, one can determine that
the greater the CIP content, the stronger the MRP’s damping.
With subjective understanding, we think that the addition of
the CIP into the polyurethane matrix introduces the internal
friction between the CIP and the matrix as well as the interparticle friction of the CIP. As theCIP content increases, the
effect of the internal friction gets stronger and stronger, which
contributes to the damping of the MRP.
To study the shear rate’s effect on the mechanical
behavior of MRP, MRP-60 is chosen as a test sample, and the
shear strain amplitude is set as a constant of 100%. The
mechanical bahavior of the MRP-60 under different shearingrate conditions without an external magnetic field can be
found in figure 6. In each test, the shear strain progresses
linearly from an initial 0% to 100%, and the shape of the
shear stress-strain loop is very similar to the test (MRP-60, γ ̇
= 0.040 s−1, A0 = 100%). One can clearly recognize that the
larger the shear rate, the larger the area of the shear stressstrain loop. Corresponding to the shear stress-strain loops of
the shear rates γ ̇ = 0.083, 0.040, 0.020 and 0.005 s−1, the
sizes of the areas of the loops are 56.40, 27.82, 12.56 and
1.97 kJ · m−3, respectively. It is again shown that the MRP is a
highly rate-dependent damping material. In other words, the
larger the shear rate, the more the energy absorption and the
higher the damping performance. Therefore, the rate-dependent mechanical behavior of the MRP must be take into
account for the design of dampers in which the MRP can be
prospectively used.
The effect of the shear strain amplitude on the MRP’s
mechanical behavior can be intuitively known from figure 7;
the larger the shear-strain amplitude, the higher the damping
performance. In the test, the magnitude of the shear rate is set
as a constant of 0.040 s−1. The shear stress-strain curves of the
MRP-60 under different shear-strain amplitudes without an
external magnetic field can be seen in figure 7. The effect of
different shear strain amplitudes of 10%, 25%, 50%, 75% and
100% are comparatively studied. When the shear strain
amplitude is small, e.g. 10% (the green-rhombus one in
figure 7), the shear stress changes sharply with the shear
strain, drawing a sharp hysteresis loop. When the shear strain
amplitude is larger than 25%, the shear stress-strain loop gets
increasingly stouter with the increasing shear strain amplitude, while the maximum shear stress hardly changes. In other
words, the MRP mainly gets a plastic flow when the shear
strain is larger than 25%. Corresponding to the shear strain
amplitudes of 10%, 25%, 50%, 75% and 100%, the sizes of
the loops’ areas are 1.98, 5.86, 12.96, 19.98 and
27.83 kJ · m−3, respectively. The size of the loop area proportionally enlarges with the increasing shear strain amplitude, indicating that the damping performance of the MRP
proportionally increases with the increasing shear strain
amplitude. Usually, the larger the shear strain amplitude, the
higher the MRP’s damping performance; however, the magnitude of the shear strain amplitude is usually restricted by the
size of the damper’s external structure.
4.3. Mechanical behavior under a cyclically shearing condition
with an external magnetic field
From the previous subsection, one can determine that the
MRP is a prospective damping material for passive dampers.
But for all of this, active controlling or actuating is usually
needed and is necessary in many practical applications. As a
magneto-sensitive material, an MRP has great potential for
use in an active damper or actuator. To study the mechanical
behavior of an MRP under a cyclically and quasi-statically
shearing condition with an external magnetic field, the MRP60 is also chosen as the test sample; then, the effect of the
external magnetic strength and shear rate are discussed.
Before the test, a 662.6 kA m−1 magnetic field is applied and
kept for 300 s to adequately configure the internal particle6
Smart Mater. Struct. 23 (2014) 105028
T Liu et al
Figure 8. The shear stress-strain loops of the MRP-60 under a
different external magnetic field with a constant magnitude of shear
rate |γ| = 0.040 s−1 and a shear strain amplitude A0 = 100%. The inset
shows the analytical model of the MRP-60 under an external
magnetic field.
Figure 9. The mechanical behavior of the MRP-60 under a different
shearing condition with or without an external 293.0 kAm−1
magnetic field.
this curve, the shear stress sharply increases with the
increasing the shear strain from the initial 0% and then progresses to the maximum stress in a fluctuating way. In the
meantime, the configuration of the internal particle-formed
microstructure changes greatly along with the shear stress’s
increasing size and wavelike progression. After the shear
strain gets to the maximum and begins to inversely approach
0%, the shear stress abruptly drops and undergoes a fluctuating process in the subsequent ten seconds; then, it gradually
approaches the inverse maximum. In the fluctuating process
of the shear stress, the internal microstructure undergoes a
very complex changing process, which includes the chain-like
microstructure’s complex rupture and reconstruction. Moreover, it is noticeable that the maximum of the shear stress can
be enhanced after several shearing cycles. To the best of our
knowledge, the cyclic shearing load induces a tighter microstructure along the direction of the external magnetic field,
which contributes to the maximum shear stress. The macroscopic analytical model of this mechanical behavior can be
qualitatively described in the top-left inset. Corresponding to
the black, red and blue curves, the areas of the three colored
loops are 24.24, 39.87 and 66.82 kJ · m−3, respectively, which
indicates that the external magnetic field has a strong influence on the damping performance of the MRP.
In contrast to the mechanical behavior of the MRP-60
under no external magnetic field, the shear rate dependent
mechanical behavior of the MRP-60 under a 293.0 kA m−1
magnetic field is shown in figure 9. In the absence of an
external magnetic field, the mechanical behavior of the MRP60 can be described using equation (1); the areas of the shear
stress-strain loops 0.005, 0.020, 0.040 and 0.083 s−1 (indicated by the solid black lines in figure 9) are 1.97, 12.56,
27.82 and 56.40 kJ · m−3, respectively. Under the
293.0 kA m−1 magnetic field, the mechanical behavior can be
qualitatively described using equation (2); the areas of the
shear stress-strain loops are 16.08, 40.48, 67.30 and
124.17 kJ · m−3, respectively. Correspondingly, the relative
magneto-induced enhancing effects are 716.2%, 222.3%,
assembled microstructure in the MRP-60. The varying process of the magneto-induced normal stress is compared to the
cyclically shearing process under an external magnetic field
and is discussed.
The shear stress-strain curve of the MRP-60 under a
different external magnetic field can be found in figure 8. In
each test, the shear strain continuously and repeatedly progresses four cycles with the constant magnitude of shear rate
γ ̇ = 0.040 s−1 and the shear-strain amplitude A0 = 100%. In
the absence of an external magnetic field (i.e. H = 0.0 kA m−1,
as the black curve in figure 8 shows), the shear stress-strain
loops are oblate and well repeated. This mechanical behavior
can be described via the analytical model in the bottom right
in figure 8. By comparing the analytical model in figure 8 to
the MRP model in figure 5, it is also found that the preconfigured MRP would behave similarly to the initial MRP
with a randomly dispersed carbonyl iron powder after the
external magnetic field is switched off since the microstructure that remained after the field was removed would
quickly be disrupted upon shear or squeeze. The shear stressstrain relationship under an external 95.6 kA m−1 magnetic
field is shown as the red curve. From figure 2, one can
determine that the 95.6 kA m−1 magnetic field can only drive
a very slow evolution of the microstructure in the MRP. That
is to say, the evolution of the internal microstructure of the
MRP is mainly affected by shear strain. The external magnetic field slightly affects the strength of the interparticle
magnetic interaction and mainly contributes to the initial
elasticity of the MRP. In the post-yield range, the magnetoinduced interparticle interaction is not strong enough to resist
the microstructural evolution induced by the shear deformation. Thus, the ‘Red, 95.0 kA m−1’ curve increases its height
and keeps its shape quite similar to that of the ‘Black,
0.0 kA m−1’ curve. Under an external 293.0 kA m−1 magnetic
field (the strength is enough to drive a quick variation of the
internal microstructure of the MRP), the mechanical behavior
of the MRP-60 is shown as the ‘Blue, 293.0 kA m−1’ curve. In
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Smart Mater. Struct. 23 (2014) 105028
T Liu et al
141.9% and 120.2%, respectively. The relative magnetoinduced enhancing effect is defined as the ratio of the area
difference between the red dot-dash loop and the black solid
loop to the area of the black solid loop. For example, in the
top-right subfigure of figure 9, the area of the black solid loop
is firstly calculated (12.56 kJ · m−3); then, the area of the red
dot-dash loop (40.48 kJ · m−3) is calculated. Thus, the defined
relative magneto-induced enhancing effect is calculated as
(40.48-12.56)/12.56 × 100% ≈ 222.3%. This value indicates
how much the damping of the MRP is enhanced by the
applied field. One can see that the relative magneto-induced
enhancement decreases with the increasing shear rate, though
the damping itself is greatly enhanced. In the case of a low
shear rate condition (e.g. γ ̇ = 0.005 s−1), the external magnetic field has relatively enough time (e.g. 200 s) to drive the
microstructural evolution, resulting in the macroscopic
mechanical behavior that mainly depends on the magnetoinduced microstructure and its evolution. In other words, the
enhancement of the shear stress mainly results from the
magneto-induced enhancement of the initial shear yield stress.
In the case of a high shear rate condition (e.g. γ ̇ = 0.083 s−1),
the shear strain progresses to the maximum 100% from the
initial 0% in a relatively short time (e.g. 12 s). The external
magnetic field can only drive the microstructure’s evolution
to some extent, and the shear-induced deformation mainly
dominates the microstructure’s evolution. The enhancement
of the macroscopic shear stress mainly results from the contribution of the magneto-enhanced initial yield shear stress
and the contribution of the shear rate-enhanced shear stress.
With the increasing shear rate, the contribution of the shear
rate-enhanced shear stress sensitively enlarges significantly,
while the contribution of the magneto-enhanced shear stress
changes little with the increasing shear rate as the magnetoenhanced shear stress mostly depends on the external magnetic strength. This results in a decreased relative magnetoinduced effect with the increased shear rate.
From section 3, one can see that the MRP’s shape and the
internal particle-formed microstructure can be dramatically
tuned by the external magnetic field, inducing the axial
(normal) stress along the field’s direction. Thus, it is attractive
to study the magneto-induced normal stress in the cyclically
shearing process of the MRP. Corresponding to figure 8, the
evolution of the magneto-induced normal stress with the
cyclically shearing process under a different external magnetic field is shown in figure 10. In the absence of an external
magnetic field, the normal stress σn is nearly zero and changes
little in the shearing process. When the external magnetic field
is H = 95.6 kA m−1, the initial magneto-induced normal stress
is about 2.5 kPa. In the beginning range (i.e. the shear strain
increases from the initial 0% to about 5%), the normal stress
slightly increases. This may result from the contribution of the
chain-like microstructures’ interaction. With the shear strain
continuing to enlarge, the normal stress gradually goes down.
This effect results from the complex coupled effects of the
reduction of the normal stress component (as the preformed
microstructure inclines), the rupture of the chain-like microstructure, etc. After the chain-like microstructure is lengthened, the interparticle gap in the chain-like microstructure
Figure 10. The magneto-induced normal stress’s variation in the
MRP-60 with the cyclically varying shear strain under a different
external magnetic field. The purple dash arrow denotes the initial
varying direction of the normal stress. The inset shows the initial
preformed microstructure in the MRP.
appears. The gap induces a negative contribution to the normal stress since the attracting interaction between the upper
particle and the lower particle still exists. When the shear
strain inversely approaches 0% after it reaches the maximum,
the internal particle-formed microstructure begins to reconstruct and contribute to the normal stress again. However, the
reconstructed microstructure will rupture again after the
reconstructed structure is squeezed to a certain extent. This
effect results in the appearance of the peaks of magnetoinduced normal stress. When H = 293.0 kA m−1 (i.e. the
magnetic strength is enough to timely tune the internal
microstructure of the MRP), the initial magneto-induced
normal stress enhances greatly to 12.4 kPa, and the normal
stress changes in a large range from 4.3 to 24.5 kPa. The
reconstruction and the rupture of the internal particle-formed
microstructure progress simultaneously, and their contributions to the macroscopic normal stress are contrary. When the
effect of the rupture (including the microstructure’s incline) is
larger than that of the reconstruction, the normal stress will
drop. Contrarily, the normal stress will rise when the effect of
the reconstruction is larger than that of the rupture. It can
clearly be seen that the magneto-induced normal stress can be
tuned in a large range and will enhance significantly after
several cycles. To the best of our knowledge, this enhancement may result from the contribution of separated particles
and short chains that assemble into main chain-like or column-like structures. This actuating mode in the normal or
axial direction using transverse torsional shear is a new
actuating mode in magnetorheology.
5. Conclusions
In this work, the magneto-induced large deformation effect of
the MRP is reported, and the magneto-damping performance
of the MRP under a quasi-statically shearing condition is
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T Liu et al
studied. From the study on the magneto-induced large
deformation of an MRP, one can determine that the external
magnetic field can tune the deformation of the MRP, and it is
shown that the magneto-induced stress in the MRP drives the
deformation. For the polyurethane-based MRP composited
with 70 wt % CIP, the magneto-induced axial stress in the
MRP can be tuned in a large range from 0.0 kPa to 55.4 kPa
by a 662.6 kA m−1 magnetic field. From the study on the
mechanical behavior of the MRP under a quasi-statically
shearing condition, it is demonstrated that an MRP possesses
a magneto-sensitive plastic malleability, and the magnetomechanical behavior of an MRP can be described using a
modified Bingham fluid model. The damping performance of
the MRP has a significant positive correlation with the
external magnetic strength, the shear rate, the CIP content and
the amplitude of the shear strain. For an MRP with 60 wt %
CIP, the relative magneto-enhanced damping effect can reach
as high as 716.2% under an external 293.0 kA m−1magnetic
field. Moreover, one can recognize that the magneto-induced
normal stress can be tuned in a large range from 4.3 kPa to
24.5 kPa along with the cyclically shearing process, and the
normal stress will be significantly enhanced after several
shearing cycles. This work demonstrates that MRPs have
great potential for use in prospective dampers and actuators.
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Acknowledgments
The financial support of the National Natural Science Foundation of China (Grant Nos. 11125210, 11102202), the
National Basic Research Program of China (973 Program,
grant no. 2012CB937500) and the Anhui Provincial Natural
Science Foundation of China (1408085QA17) are gratefully
acknowledged.
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